The low rate TCP DoS (Shrew) and the reduction of quality (RoQ) attacks have been proved to be detrimental to the TCP traffic in the Internet. In this paper, we investigate the effect of these attacks on the QoS sensitive real time UDP traffic like VoIP. The stealthy RoQ attacks in particular are hard to detect as its periodicity is not well defined as compared to the shrew attack, and they can be launched even with the destination IP address spoofed! The attack potency formula is tailored for our work to observe the detrimental effect of the attack on the VoIP traffic. We study the effect of the attack flow on three QoS parameters of a VoIP flow, namely, the delay, the jitter, and the packet loss. We have performed extensive ns2 simulations under realistic scenarios to validate the effect of these attacks on the real time UDP traffic. Our results indicate that both these attacks are capable of driving a VoIP call from good to acceptable quality, i.e., reduction of qualify, and from acceptable quality to complete denial of service. We believe that it is critical to investigate the characteristics of any attack in order to develop sound mitigation mechanisms; this work highlights one such characteristic of the low rate DoS attack.